Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 236 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. C33×C4 | Q16 | semidirect |
| 106. C32×C4 | Dic12 | semidirect |
| 107. C32×C4 | #216 | semidirect |
| 119. C33 | #494 | semidirect |
| 157. C3×C4 | #3719 | semidirect |
| 158. C3×C4 | #3746 | semidirect |
| 166. C32 | #4699 | semidirect |
| 167. C32 | #5092 | semidirect |
| 184. C4 | #88800 | semidirect |
| 187. C3 | #10590386 | semidirect |
| 188. C3 | #10592398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C3×#64078 | 2 |
| C2×#88800 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #10592398 | 3 |
| #10590386 | 3 |